Gramian-based uniform convergent observer for stable LTV systems with delayed measurements

In this work, an observer for a linear time-varying system with delayed measurements is developed. The delay is assumed to be unknown, bounded, and it can be time-varying with no restriction on its rate of change. The observer uses auxiliary signals related to the constructibility Gramian of the sys...

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Bibliographic Details
Published in:International journal of control 2020-02, Vol.93 (2), p.226-237
Main Authors: Rueda-Escobedo, Juan G., Ushirobira, Rosane, Efimov, Denis, Moreno, Jaime A.
Format: Article
Language:English
Subjects:
Automatic
Computer simulation
Convergence
Delay
delayed output
Engineering Sciences
Initial conditions
linear time-varying systems
Observer
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Summary:In this work, an observer for a linear time-varying system with delayed measurements is developed. The delay is assumed to be unknown, bounded, and it can be time-varying with no restriction on its rate of change. The observer uses auxiliary signals related to the constructibility Gramian of the system and it contains nonlinearities that provide a uniform fixed-time convergence to a bounded region in the estimation error coordinates. This means that the convergence time can be bounded by a positive constant which is independent from the initial conditions and the initial time. This property is new for the addressed class of systems. The ultimate bound of the estimation error depends on the maximum difference between the nominal output and the delayed one, and not directly on the delay size or its time derivative. These properties are illustrated in a numerical simulation.
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2019.1569256